There are 1000 lockers in the long hall of Westfalls High. In preparation for the beginning of school, the janitor cleans the lockers and paints fresh numbers on the locker doors. The lockers are numbered from 1 to 1000. When the 1000 Westfalls High students arrive from summer vacation, they decide to celebrate the beginning of school by working off some energy. The first student, student 1, runs down the row of lockers and opens every door. Student 2 closes the doors of lockers 2,4, 6, and 8, and so on to the end of the line. Student 3 changes the state of the doors of lockers 3, 6, 9, 12 and so on to the end of the line. (The student opens the door if it is closed and closes the door if it is open.) Student 4 changes the state of the doors of lockers 4, 8, 12, 16, and so on. Student 5 changes the state of every fifth door, student 6 changes the state of every sixth door, and so on until all 1000 students have a turn. When the students are finished, which locker doors are open?